Life can get pretty lonely when you're in a new town and haven't really established any social connections, but that doesn't mean it has to stay lonely. Your ability to meet people your age in a new town really depends on your motivation and your willingness to put yourself out there.
Expand your definition of "friends your age". That old chestunut -- "you're only as young as feel" -- has some truth to it. You may find that you can actually have very rewarding relationship with those who are significantly older than yourself, or perhaps several years your junior. While this relationship may turn into more of a mentorship given the difference in maturity and experience, your shared interests, passions or values could create a mutually beneficial partnership.
Go online. The first place many people will turn to when seeking to expand their social network is the internet. Meetup (meetup.com) is an online community of people who are interested in meeting others who share their interests. See what Meetups are available in your community. If none of them appeal to you, start your own. Couchsurfing (couchsurfing.com) is another expanding international network that, beyond providing free lodging to travelers, seeks to build community all over the globe. Check out the scene in your town. Craigslist lists opportunities for friendly encounters as well as local events and activities. Introduce yourself to town by posting one of your own and detailing what kind of friends you are looking for. Does the internet sketch you out? Try posting a flier at your local café in stead.
Go it alone. If a great band is coming to town and you don't have a friend to go with, buy a ticket and go by yourself. The same goes for the art gallery opening on the corner, the street-wide yard sale, and the minor league baseball game. The more you are willing to put yourself out there, the greater chance you stand of fortuitously meeting someone and striking up a friendship. Barring any big events, don't hesitate to drop down to the local pub or the corner café; someone is bound to notice you and say hi.
Take a risk. You may have to muster up the courage to strike up some conversations with strangers yourself, be it at the gym, in the park or at the grocery store. Practice saying things like, "Excuse me, is this seat taken?" or "I'm here alone; do you mind if I join you?" If they react coldly, you don't want to be friends with them anyway.
Do things you love. One way to meet people is through your hobbies and pastimes. The people you meet through are guaranteed to share your interests. Take a regular yoga class, tennis, boxing or painting. You might also explore volunteer opportunities in your area. Volunteering your time for a worthy cause has the added benefit that the people you meet are probably also community-minded and interested in helping others.
Ask for suggestions. Don't be shy about speaking to your coworkers, neighbors or landlord about your dilemma and ask them to hook you up with their friends, family and neighbors who are roughly the same age and who might enjoy getting to know you. Carry around a little phone book so you can write in your new acquaintances' contact information.